已知函数f(x)=cosx/cos(π/6-x),则f(x)+f(π/3-x)的值为
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已知函数f(x)=cosx/cos(π/6-x),则f(x)+f(π/3-x)的值为
f(π/3-x)=cos(π/3-x)/cos(π/6-(π/3-x))
=cos(π/3-x)/cos(x-π/6)
=cos(π/3-x)/cos(π/6-x) 注:cosx = cos(-x)
所以:
f(x)+f(π/3-x) = cosx/cos(π/6-x) + cos(π/3-x)/cos(π/6-x)
= [cosx + cos(π/3-x)]/cos(π/6-x)
= 2cos(π/6)cos(π/6-x)/cos(π/6-x)
= 2cos(π/6)
=√3
=cos(π/3-x)/cos(x-π/6)
=cos(π/3-x)/cos(π/6-x) 注:cosx = cos(-x)
所以:
f(x)+f(π/3-x) = cosx/cos(π/6-x) + cos(π/3-x)/cos(π/6-x)
= [cosx + cos(π/3-x)]/cos(π/6-x)
= 2cos(π/6)cos(π/6-x)/cos(π/6-x)
= 2cos(π/6)
=√3
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